166 



SYMPOSIUM ON AERONAUTICS. 



on release the card immediately tips downward behind, and as it 

 goes ahead with great velocity receives more than enough upthrust 

 for its own sustentation, and is actually able to rise, although pulled 

 down by the string. 



I come now to perhaps the most important dynamical aspect of 

 aviation, that is the question of stability of flight. Stability of equi- 

 librium is a familiar notion, and exists when a system, if displaced, 

 tends to return to its former position, generally performing small 

 oscillations about it which die away, leaving it in its equilibrium 

 position. Thus a pea at the bottom of a bowl is in stable equi- 

 librium, but on top of a sphere, though in equilibrium, is unstable, 



Fig. 6 



because if slightly displaced it will not return, but will roll off. 

 Stability of motion may be similarly defined. If an aeroplane is in 

 flight, and is slightly displaced in position or direction, will it tend 

 to resume its position or will it tend to leave it more and more? 

 Consider what happens when it tips forward and downward. If 

 the center of pressure n:oves forward wdien the angle of attack is 

 less it will tend to turn the plane backward, so as to resume its 

 former position. So far then the motion is stable. As it tips 

 forward the angle of attack becomes sm.aller, the sustaining force 

 becomes less, and the aeroplane sinks, but when tipped back again 

 it rises once more. Thus the path oscillates about a horizontal Hne. 

 But a rigid body has six ways of moving: forward and back, side- 

 wise right and left, and vertically up and down, making three, to- 

 gether with three ways of turning, rolling about an axis fore and 

 aft, pitching about a transverse axis, and yaw'ing, or turning about 

 the vertical. If any of these six motions arc disturbed, bow will 

 the motion be afi"cctcd? It is easily shown that a change in any of 



